QDs are robust and spectrally narrow quantum emitters that have attracted significant interest as solid-state qubits. Various approaches have been pursued for storage and manipulation of quantum information in QDs. One approach has been to exploit neutral exciton transitions that can be controlled all-optically to enable both single qubit operations as well as two-qubit operations between distinguishable excitons in a QD 12 .More recently, major progress has been achieved in coherently manipulating highly 2 stable spin states of a charged QD, which promise significantly longer coherence times [13][14][15][16][17] .Another important property of QDs is that they can be coupled to optical nano-cavities in the strong coupling regime 18-21 where a QD can modify the cavity spectral response 22,23 , enabling novel applications such as ultra-fast low photon number optical switching [24][25][26] and single QD lasing 27 . Furthermore, the strong coupling regime can be exploited to interface these solid-state qubits with a flying photonic qubit through direct QD-photon quantum logic operations, as proposed in a number of theoretical works [6][7][8] . In order to realize this capability, three essential requirements must be met. First, the QD must possess two quantum states whose coherence time is long compared to the interaction time with the photonic qubit. Second, the qubit states of the QD must be coherently controllable. Finally, the qubit state of the QD must have a strong effect on the quantum state of the photon. Achieving these requirements in a solid-state photonic platform has remained an outstanding challenge.In this letter we demonstrate that a QD strongly coupled to an optical nanocavity can satisfy all of the above requirements, implementing a solid-state qubit in a cavity system that can perform quantum gates on a photon at picosecond timescales. We experimentally demonstrate a cNOT logic gate between the QD and a photonic qubit, which is a universal quantum operation that can serve as a general light-matter interface for remote entanglements and distributed quantum computation. Our device is composed of an indium arsenide (InAs) QD strongly coupled to a photonic crystal cavity. Fig. 1a illustrates the level structure of an InAs QD, which includes a ground state (|g) and two bright exciton states, labelled |+ and |-, representing the two anti-aligned spin configurations of the electron and hole. The optical transitions from the ground state to the two bright excitons, denoted  + and  -, exhibit right and left circularly polarized emission respectively at high magnetic field. For all measurements performed in this work the biexciton transition is significantly detuned and can therefore be ignored, enabling the QD to be treated as a three-level system. By applying a magnetic field in the sample growth direction (Faraday configuration), the  + transition can be tuned on resonance with the cavity while the  -transition remains detuned 28 . In this configuration, 3 states |g and |- are the qubit stat...

We demonstrate resonant coupling of a Mollow triplet sideband to an optical cavity in the strong coupling regime. We show that, in this regime, the resonant sideband is strongly enhanced relative to the detuned sideband. Furthermore, the linewidth of the Mollow sidebands exhibits a highly nonlinear pump power dependence when tuned across the cavity resonance due to strong resonant interactions with the cavity mode. We compare our results to calculations using the effective phonon master equation and show that the nonlinear linewidth behavior is caused by strong coherent interaction with the cavity mode that exists only when the Mollow sideband is near cavity resonance.

We demonstrate strong coupling between two indium arsenide (InAs) quantum dots (QDs) and a photonic crystal cavity by using a magnetic field as a frequency tuning method. The magnetic field causes a red shift of an exciton spin state in one QD and a blue shift in the opposite exciton spin state of the second QD, enabling them to be simultaneously tuned to the same cavity resonance. This method can match the emission frequency of two QDs separated by detunings as large as 1.35 meV using a magnetic field of up to 7 T. By controlling the detuning between the two QDs we measure the vacuum Rabi splitting (VRS) both when the QDs are individually coupled to the cavity, as well as when they are coupled to the cavity simultaneously. In the latter case the oscillator strength of two QDs shows a collective behavior, resulting in enhancement of the VRS as compared to the individual cases. Experimental results are compared to theoretical calculations based on the solution to the full master equation and found to be in excellent agreement.